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Elementary Differential Equations and Boundary Value Problems 10th Edition International Student Version [Pehme köide]

(Rensselaer Polytechnic Institute), (Rensselaer Polytechnic Institute)
  • Formaat: Paperback / softback, 832 pages, kõrgus x laius x paksus: 256x205x26 mm, kaal: 1397 g
  • Ilmumisaeg: 04-Dec-2012
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1118323610
  • ISBN-13: 9781118323618
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  • Formaat: Paperback / softback, 832 pages, kõrgus x laius x paksus: 256x205x26 mm, kaal: 1397 g
  • Ilmumisaeg: 04-Dec-2012
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 1118323610
  • ISBN-13: 9781118323618
Teised raamatud teemal:
The 10th edition of Elementary Differential Equations and Boundary Value Problems, like its predecessors, is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical, sometimes intensely practical, and often somewhere in between.  The authors have sought to combine a sound and accurate (but not abstract) exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, the 10th edition includes new problems, updated figures and examples to help motivate students.

The book is written primarily for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year of study. The main prerequisite for reading the book is a working knowledge of calculus, gained from a normal two?(or three) semester course sequence or its equivalent. Some familiarity with matrices will also be helpful in the chapters on systems of differential equations.
Chapter 1 Introduction
1(30)
1.1 Some Basic Mathematical Models; Direction Fields
1(9)
1.2 Solutions of Some Differential Equations
10(9)
1.3 Classification of Differential Equations
19(7)
1.4 Historical Remarks
26(5)
Chapter 2 First Order Differential Equations
31(106)
2.1 Linear Equations; Method of Integrating Factors
31(11)
2.2 Separable Equations
42(9)
2.3 Modeling with First Order Equations
51(17)
2.4 Differences Between Linear and Nonlinear Equations
68(10)
2.5 Autonomous Equations and Population Dynamics
78(17)
2.6 Exact Equations and Integrating Factors
95(7)
2.7 Numerical Approximations: Euler's Method
102(10)
2.8 The Existence and Uniqueness Theorem
112(10)
2.9 First Order Difference Equations
122(15)
Chapter 3 Second Order Linear Equations
137(84)
3.1 Homogeneous Equations with Constant Coefficients
137(8)
3.2 Solutions of Linear Homogeneous Equations; the Wronskian
145(13)
3.3 Complex Roots of the Characteristic Equation
158(9)
3.4 Repeated Roots; Reduction of Order
167(8)
3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients
175(11)
3.6 Variation of Parameters
186(6)
3.7 Mechanical and Electrical Vibrations
192(15)
3.8 Forced Vibrations
207(14)
Chapter 4 Higher Order Linear Equations
221(26)
4.1 General Theory of nth Order Linear Equations
221(7)
4.2 Homogeneous Equations with Constant Coefficients
228(8)
4.3 The Method of Undetermined Coefficients
236(5)
4.4 The Method of Variation of Parameters
241(6)
Chapter 5 Series Solutions of Second Order Linear Equations
247(62)
5.1 Review of Power Series
247(7)
5.2 Series Solutions Near an Ordinary Point, Part I
254(11)
5.3 Series Solutions Near an Ordinary Point, Part II
265(7)
5.4 Euler Equations; Regular Singular Points
272(10)
5.5 Series Solutions Near a Regular Singular Point, Part I
282(6)
5.6 Series Solutions Near a Regular Singular Point, Part II
288(8)
5.7 Bessel's Equation
296(13)
Chapter 6 The Laplace Transform
309(50)
6.1 Definition of the Laplace Transform
309(8)
6.2 Solution of Initial Value Problems
317(10)
6.3 Step Functions
327(9)
6.4 Differential Equations with Discontinuous Forcing Functions
336(7)
6.5 Impulse Functions
343(7)
6.6 The Convolution Integral
350(9)
Chapter 7 Systems of First Order Linear Equations
359(92)
7.1 Introduction
359(9)
7.2 Review of Matrices
368(10)
7.3 Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors
378(12)
7.4 Basic Theory of Systems of First Order Linear Equations
390(6)
7.5 Homogeneous Linear Systems with Constant Coefficients
396(12)
7.6 Complex Eigenvalues
408(13)
7.7 Fundamental Matrices
421(8)
7.8 Repeated Eigenvalues
429(11)
7.9 Nonhomogeneous Linear Systems
440(11)
Chapter 8 Numerical Methods
451(44)
8.1 The Euler or Tangent Line Method
451(11)
8.2 Improvements on the Euler Method
462(6)
8.3 The Runge--Kutta Method
468(4)
8.4 Multistep Methods
472(6)
8.5 Systems of First Order Equations
478(4)
8.6 More on Errors; Stability
482(13)
Chapter 9 Nonlinear Differential Equations and Stability
495(94)
9.1 The Phase Plane: Linear Systems
495(13)
9.2 Autonomous Systems and Stability
508(11)
9.3 Locally Linear Systems
519(12)
9.4 Competing Species
531(13)
9.5 Predator-Prey Equations
544(10)
9.6 Liapunov's Second Method
554(11)
9.7 Periodic Solutions and Limit Cycles
565(12)
9.8 Chaos and Strange Attractors: The Lorenz Equations
577(12)
Chapter 10 Partial Differential Equations and Fourier Series
589(88)
10.1 Two-Point Boundary Value Problems
589(7)
10.2 Fourier Series
596(11)
10.3 The Fourier Convergence Theorem
607(7)
10.4 Even and Odd Functions
614(9)
10.5 Separation of Variables; Heat Conduction in a Rod
623(9)
10.6 Other Heat Conduction Problems
632(11)
10.7 The Wave Equation: Vibrations of an Elastic String
643(15)
10.8 Laplace's Equation
658(19)
Appendix A Derivation of the Heat Conduction Equation
669(4)
Appendix B Derivation of the Wave Equation
673(4)
Chapter 11 Boundary Value Problems and Sturm-Liouville Theory
677(62)
11.1 The Occurrence of Two-Point Boundary Value Problems
677(8)
11.2 Sturm-Liouville Boundary Value Problems
685(14)
11.3 Nonhomogeneous Boundary Value Problems
699(15)
11.4 Singular Sturm-Liouville Problems
714(7)
11.5 Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion
721(7)
11.6 Series of Orthogonal Functions: Mean Convergence
728(11)
Answers to Problems 739(60)
Index 799